Question:
Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5000 × 8% × 7
= $5000 ×8/100 × 7
= 5000 × 8 × 7/100
= 40000 × 7/100
= 280000/100
= $2800
Thus, Simple Interest = $2800
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2800
= $7800
Thus, Amount to be paid = $7800 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5000
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 8% × 7)
= $5000 + ($5000 ×8/100 × 7)
= $5000 + (5000 × 8 × 7/100)
= $5000 + (40000 × 7/100)
= $5000 + (280000/100)
= $5000 + $2800 = $7800
Thus, Amount (A) to be paid = $7800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5000, the simple interest in 1 year
= 8/100 × 5000
= 8 × 5000/100
= 40000/100 = $400
Thus, simple interest for 1 year = $400
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $400 × 7 = $2800
Thus, Simple Interest (SI) = $2800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2800
= $7800
Thus, Amount to be paid = $7800 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.
(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(10) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.